Similarity estimation between nodes based on structural properties of graphs
is a basic building block used in the analysis of massive networks for diverse
purposes such as link prediction, product recommendations, advertisement,
collaborative filtering, and community discovery. While local similarity
measures, based on properties of immediate neighbors, are easy to compute, those
relying on global properties have better recall. Unfortunately, this better
quality comes with a computational price tag. Aiming for both accuracy and
scalability, we make several contributions. First, we define closeness
similarity, a natural measure that compares two nodes based on the similarity of
their relations to all other nodes. Second, we show how the all-distances sketch
(ADS) node labels, which are efficient to compute, can support the estimation of
closeness similarity and shortest-path (SP) distances in logarithmic query time.
Third, we propose the randomized edge lengths (REL) technique and define the
corresponding REL distance, which captures both path length and path multiplicity
and therefore improves over the SP distance as a similarity measure. The REL
distance can also be the basis of closeness similarity and can be estimated using
SP computation or the ADS labels. We demonstrate the effectiveness
of our measures and the accuracy of our estimates through experiments on social
networks with up to tens of millions of nodes.